We use scattering theoretic methods to prove strong dynamical and
exponential localization for one-dimensional, continuum, Anderson-type
models with singular distributions; in particular, the case of a
Bernoulli distribution is covered. The operators we consider model
alloys composed of at least two distinct types of randomly dispersed
atoms. Our main tools are the reflection and transmission coefficients
for compactly supported single-site perturbations of a periodic
background which we use to verify the necessary hypotheses of
multi-scale analysis. We show that nonreflectionless single sites lead
to a discrete set of exceptional energies away from which localization
occurs.